Abstract

An explicit representation for the surface corresponding to a shaded image is presented and proven to be correct (under standard conditions). Uniqueness of the surface is an immediate consequence. Using this representation, various iterative algorithms for shape reconstruction are derived. It has been proven that all these algorithms converge monotonically to the correct surface reconstruction, and they have been shown experimentally to be fast and robust. Some of the results of this paper extend previous ones to the case of illumination from a general direction.

This research was supported in part by National Science Foundation grants DMS-9115762, IRI-9113690, and CDA-822572.